By Sung-Eun Kim, Principal Development Engineer, Fluent Inc. and Davor Cokljat, Senior Principal Developer, Fluent Europe Ltd.

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The flow structure behind a circular cylinder predicted by FLUENT's LES model at a Reynolds number of 1.4 x 10⁵; vortical structures are colored by velocity magnitude

During the past several decades, turbulence models based on the Reynolds-averaged Navier-Stokes (RANS) equations have been the major workhorses for industrial applications. They will undoubtedly continue to serve this purpose in the foreseeable future because of their cost-effectiveness and reasonable accuracy for a wide class of flows. FLUENT offers a comprehensive suite of RANS-based models, including the k-ε and k-ω families of eddy-viscosity models, and the Reynolds stress transport model. (See, for example, the article The Prolate Spheroid Separates Turbulence Models.)

Summary of some global flow parameters predicted by FLUENT's LES model for the flow over a circular cylinder with a Reynolds number of 1.4 x 10⁵, compared with experimental results; comparisons with other numerical results can be found in Reference 3

Despite the long-established efficacy of RANS-based turbulence modeling for industrial CFD, there are many emerging, technologically important applications that RANS-based models are ill-equipped to handle, in such areas as bluff-body aerodynamics, fluid-structure interaction (FSI), aeroacoustics, material processing, and combustion dynamics. Many of these applications involve large-scale coherent flow structures (in short, large eddies) that significantly impact various aspects of the associated systems, such as energy consumption, safety, product quality, and comfort. And yet, attempts made thus far to numerically predict such flows using RANS-based models have been met with limited success. Still computationally expensive, large eddy simulation (LES) is rapidly emerging as a viable approach to addressing these challenging applications. In LES, large, energy-containing eddies are directly computed, while only the remaining smaller eddies are modeled, using a subgrid-scale (SGS) turbulence model. By contrast, RANS-based modeling is an approach in which an entire range of scales is modeled.

Near-wall turbulence structure in a channel with a Reynolds number of 180 computed using LES with the dynamic Smagorinsky subgrid scale model on a 72 x 72 x 72 mesh; an iso-surface of vortical structures is shown, colored by velocity magnitude

The LES capability has been upgraded considerably in FLUENT 6.2 with several enhancements both in numerics and SGS modeling. Among the enhancements in numerics are a high-order mass-flux interpolation scheme, a bounded central differencing (BCD) scheme, and a non-iterative time-advancement (NITA) algorithm. The new mass-flux interpolation scheme, which is a crucial component of the convection discretization scheme, significantly improves the spatial accuracy on tetrahedral meshes in particular. The BCD scheme is designed to suppress unphysical wiggles numerically introduced by the pure central differencing scheme, while preserving this scheme's non-dissipative property. In FLUENT 6.2, the BCD scheme replaces the second-order upwind scheme as the default convection discretization method when LES is activated. The NITA algorithm that obviates the need for costly outer iterations based on either approximate factorization (fractional-step method) or the idea of operator-splitting (PISO) significantly speeds up LES calculations. All of these enhancements in FLUENT 6.2 numerics make LES more accurate, robust, and efficient than ever.

The mean velocity profile (top) and normal Reynolds stress profiles (bottom) predicted by LES with the dynamic Smagorinsky model (DSM) and the dynamic turbulent kinetic energy transport model (DTKEM) for fully developed turbulent flow in a channel; the LES results are compared with DNS results (2)

In the area of subgrid-scale turbulence modeling, FLUENT 6.2 comes with two new dynamic models and a special near-wall model called WALE (wall-adapting local eddy-viscosity). The new dynamic SGS models, which have been successfully implemented in the framework of the unstructured mesh-based finite-volume method, include the dynamic Smagorinsky model (DSM) and the dynamic turbulent kinetic energy transport model (DTKEM) (1). In these dynamic models, the constants are automatically adjusted on the fly during the LES calculation, based on the resolved fields, thus requiring no user inputs. In addition, the dynamic models are fundamentally better able to represent the flow physics, such as near-wall and transitional flow effects. The WALE model is capable of representing the near-wall flow physics in a cost-effective manner without using ad hoc damping functions, often adopted in conjunction with the original Smagorinsky model.

An LES simulation of the flow and species mixing in a coaxial jet combustor (7); contours of instantaneous species concentration for a side view (a), and cross-sections 25mm (b) and 51mm (c) from the expansion

For the coaxial jet combustor, mean (above) and RMS (below) species concentrations 51mm downstream of the expansion, computed at four azimuthal locations by LES and compared to experiment (7); the experimental values at all four locations are shown

The new SGS turbulence models implemented in the framework of the unstructured mesh-based finite-volume method have been validated for a broad range of flows, from simple to highly complex. For example, a fully developed channel flow has been simulated using both the dynamic Smagorinsky model and the dynamic turbulent kinetic energy transport model, and compared to simulations done using direct numerical simulation (DNS) (2). The excellent agreement ound between the LES results and DNS confirms that the dynamic SGS models correctly reproduce the near-wall behavior of both the mean flow and turbulence quantities.

In another test case, the 3D flow past a smooth circular cylinder was computed using LES at a sub-critical Reynolds number of Re = 1.4 x 105 (3). Accurate prediction of the flow at such a high subcritical Reynolds number is not an easy task, as indicated by the scarcity of successful LES results in this Reynolds number range in the literature. According to the FLUENT results, LES reproduces the laminar separation, the transition to turbulent flow in the separated shear-layer, and the alternating vortex-shedding, all of which are typical of the subcritical regime. The global flow parameters are also predicted with a commendable accuracy (3, 4, 5, 6).

Flow and species transport are essential ingredients for modeling combustors (see the article Firing Up LES for the Sandia Flame), and the case of a swirling co-axial jet (7) has been studied using LES along with the dynamic Smagorinsky model (8). It is important to note that the entire combustor, including the swirl vanes, was modeled using a hybrid unstructured mesh. What is remarkable about the results is that LES accurately predicts not only the mean species concentration, but also the RMS species concentrations, which are very important for the combustion calculation, yet difficult to predict accurately.

DES prediction of the flow inside an open cavity; contours of instantaneous static surface pressure inside and around the cavity are shown

The third mode of the RMS pressure fluctuation along the cavity floor, compared to experimental values (10)

Resolving the near-wall region down to the viscous sublayer in LES inevitably incurs a high cost for high Reynolds number wall-bounded flows, since the length and time scales of near-wall turbulence become very small there. To reduce the computational cost of resolving the near-wall region, hybrid approaches combining RANS and LES have been proposed. In essence, these hybrid approaches try to reconcile the turbulence model with the mesh resolution, invoking a proper model - either a RANS or an SGS turbulence model - depending on the local mesh resolution. Among many variants of the RANS/LES hybrids, the one called detached-eddy simulation (DES) has become increasingly popular. FLUENT has been offering a DES capability (9) based on the oneequation eddy-viscosity transport model of Spalart and Allmaras (10) for some time. In the near-wall region, the DES model reduces to the original RANS model of Spalart and Allmaras, while it acts as a subgrid-scale turbulence model away from the wall.

As for LES, the DES capability has been extensively tested and validated for a broad range of high Reynolds number flows, including the separated flow past an airfoil, open-cavity flow, and the flow around bluff bodies such as trucks (see the article Making Trucking Less of a Drag). For the case of a three-dimensional open cavity, DES successfully reproduced three modes of pressure oscillations (resonant frequencies) on the cavity ceiling that were identified in an experiment for this configuration (11). Each modal band is calculated by processing the power spectral density, using frequencies that bracket the peak. The RMS pressure distributions along the cavity ceiling for all three modes were found to agree very well with the experimental data.

Besides the enhancements in numerics and SGS modeling in FLUENT 6.2, the utility to obtain fluctuating velocity components, used to compute inlet velocity boundary conditions, has been upgraded. Two new techniques are available for computing the quasi-random fluctuating velocity field using turbulence quantities such as the turbulence intensity, length-scale, turbulent kinetic energy, Reynolds stresses, and rate of turbulent dissipation, some of which are readily available from RANS computations. The resulting fluctuating velocity fields reproduce the statistics (up to second-order, depending on the turbulence data provided) and are far more realistic than those obtained from random number generation.

References:

1. S.-E. Kim, AIAA Paper 2004, no. 2004-2548.
2. J. Kim, P. Moin, R. Moser, JFM 1987, 177, 133-166.
3. S.-E Kim, Prediction of Unsteady Loading on a Circular Cylinder in High Reynolds Number Flows Using LES. 24th International Conference on Offshore Mechanics and Artic Engineering, June 12-16, 2005, Halkidiki, Greece.
4. M. Breuer, Int. J. Heat Fluid Flow 2000, 21, 648-654.
5. A. Travin, M. Shur, M. Strelets, P. Spalart, Flow Turb. Comb. 2000 63, 293-313.
6. M.M. Zdravkovich, Flow Around Circular Cylinders;. Oxford University Press: Oxford, UK, 1997; pp 163-200.
7. R.J. Roback, ; B.V. Johnson, Mass and Momentum Turbulent Transport Experiments with Confined Swirling Coaxial Jets. NASA Contractor Report CR-168252, August 1983.
8. S.-E Kim, X. Zhu, S. Orsino, FEDSM2005 - 77085; to be presented at the ASME 2005 Fluid Engineering Division Summer Meeting and Exhibition , June 19-23, 2005, Houston, TX.
9. D. Cokljat, F. Liu, AIAA Paper 2002, no. 2002-0590.
10. P.R. Spalart and S.R. Allmaras, A One Equation Turbulence Model for Aerodynamic Flows, La Recherche Aerospatiale, No. 1, p. 5-21, 1994.
11. Experimental data for the open cavity provided by QinetiQ, funded by UK MOD Applied Research Program.

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